00:01
In this problem, we want to write the equation of a line that's perpendicular to our given line and passes through the 0 .5 -9.
00:05
So first, to find a line that's perpendicular, we first need to think about the slope of our given line.
00:12
So i'm going to first rewrite the given equation in slope intercept form, so i can analyze the slope more easily.
00:18
So subtracting x from both sides gives me 7y equals negative x plus 12.
00:23
Then divide every term by 7.
00:25
That gives me y equals negative x over 7 is the same as saying like, negative 1 over 7x plus 12 over 7.
00:35
So the slope of this line, we'll call this line 1, so slope 1 equals negative 1 7.
00:42
Our new slope, our new line that we're going to write the equation of, we'll call it line 2.
00:48
The slope of the new line, to be perpendicular, has to be the opposite reciprocal.
00:53
So reciprocal means we flip the fraction, so 7 over 1, and opposite means we change the sign.
00:59
So negative becomes positive...